HYSBZ1036 [ZJOI2008]树的统计（树链剖分）

将树通过树链剖分转化成线性序列，用线段树维护最值，和值即可。

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int N = 3e4 + 10;
  4 int n, m, head[N], to[N << 1], nxt[N << 1], tot;
  5 int total, fa[N], dep[N], size[N], son[N], top[N];
  6 int w[N], id[N], rev[N];
  7 int Max, Sum;
  8 struct node{
  9     int mx, sum;
 10 }t[N << 2];
 11 void add(int x, int y) {
 12     nxt[++ tot] = head[x]; head[x] = tot; to[tot] = y;
 13 }
 14 void dfs1(int u, int f) { //求dep,fa,size,son
 15     size[u] = 1;
 16     for (int i = head[u]; i; i = nxt[i]) {
 17         int v = to[i];
 18         if (v == f) continue;
 19         dep[v] = dep[u] + 1;
 20         fa[v] = u;
 21         dfs1(v, u);
 22         size[u] += size[v];
 23         if (size[v] > size[son[u]]) son[u] = v;
 24     }
 25 }
 26 void dfs2(int u, int t) { //求top,id,rev
 27     top[u] = t;
 28     id[u] = ++ total; // u对应的dfs序下标
 29     rev[total] = u;   // dfs序下标对应的u
 30     if (!son[u]) return ;
 31     dfs2(son[u], t);//先沿重儿子dfs
 32     for (int i = head[u]; i; i = nxt[i]) {
 33         int v = to[i];
 34         if (v != fa[u] && v != son[u]) dfs2(v, v);
 35     }
 36 }
 37 namespace SegmentTree {
 38     #define mid ((l + r) >> 1)
 39     #define lson k << 1, l, mid
 40     #define rson k << 1 | 1, mid + 1, r
 41     void pushup(int k) {
 42         t[k].mx = max(t[k << 1].mx, t[k << 1 | 1].mx);
 43         t[k].sum = t[k << 1].sum + t[k << 1 | 1].sum;
 44     }
 45     void build(int k, int l, int r) {
 46         if (l == r) {
 47             t[k].mx = t[k].sum = w[rev[l]];
 48             return ;
 49         }
 50         build(lson), build(rson);
 51         pushup(k);
 52     }
 53     void update(int k, int l, int r, int pos, int v) {
 54         if (l == r) {
 55             t[k].mx = t[k].sum = v;
 56             return ;
 57         }
 58         if (pos <= mid) update(lson, pos, v);
 59         else update(rson, pos, v);
 60         pushup(k);
 61     }
 62     void query(int k, int l, int r, int L, int R) {
 63         if (L <= l && R >= r) {
 64             Max = max(Max, t[k].mx);
 65             Sum += t[k].sum;
 66             return ;
 67         }
 68         if (L <= mid) query(lson, L, R);
 69         if (R > mid) query(rson, L, R);
 70     }
 71     void ask(int u, int v) {
 72         while (top[u] != top[v]) {
 73             if(dep[top[u]] < dep[top[v]]) swap(u, v);
 74             query(1, 1, total, id[top[u]], id[u]);
 75             u = fa[top[u]];
 76         }
 77         if (dep[u] > dep[v]) swap(u, v);
 78         query(1, 1, total, id[u], id[v]);
 79     }
 80 }
 81 using namespace SegmentTree;
 82 int main() {
 83     int x, y; char str[10];
 84     scanf("%d", &n);
 85     for (int i = 1; i < n; i ++) {
 86         scanf("%d %d", &x, &y);
 87         add(x, y), add(y, x);
 88     }
 89     for (int i = 1; i <= n; i ++) scanf("%d", &w[i]);
 90     dep[1] = 1;
 91     dfs1(1, 0);
 92     dfs2(1, 1);
 93     build(1, 1, total);
 94     scanf("%d", &m);
 95     for (int i = 1; i <= m; i ++) {
 96         scanf("%s", str);
 97         scanf("%d %d", &x, &y);
 98         if(str[0] == 'C') update(1, 1, total, id[x], y);
 99         else {
100             Sum = 0;
101             Max = -0x3f3f3f3f;
102             ask(x, y);
103             if (str[1] == 'M') printf("%d\n", Max);
104             else printf("%d\n", Sum);
105         }
106     }
107     return 0;
108 }